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Optimal Designs for Estimating Slopes

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Introduction

In classical designs, comparison of the treatment effects is of primary interest. Response surface designs are concerned with experiments in which treatments are combinations of various levels of factors that are quantitative. Consequently, the response is assumed to be a smooth function of the factors and the experimenter is usually interested in estimating the absolute response at various points in the factor space. However, even in response surface designs, sometimes the experimenter may have greater interest in estimating the differences between response at various points rather than the response at individual locations (Herzberg 1967; Box 1980; Huda 1985). If differences in response at points close together in the factor space are involved, estimation of local slopes of the response surface becomes important. Optimal designs for estimating slopes are concerned with developing various meaningful optimality criteria and deriving designs that are best according to these...

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References and Further Reading

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Huda, S. (2011). Optimal Designs for Estimating Slopes. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_429

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